following Niven [1]}, or more recently Janovsk\(\acute{a}\)  and Opfer [2]}, its
companion polynomial is defined by
\(q_{2n}(x)=\sum _{j,k=0}^n\bar{q}_jq_kx^{j+k}=\sum _{k=0}^{2n}b_kx^k,\textrm {where}\ b_k=\sum _{j=max(0,k-n)}^{min(k,n)}\bar{q}_jq_{k-j}\in \mathbb {R}.\) 
